| Scenario | Probability | Return |
|---|---|---|
| Excellent | 25% | 31.00% |
| Good | 45% | 14.00% |
| Poor | 25% | −6.75% |
| Crash | 5% | −52.00% |
FIN 223 Lecture 1
University of Wollongong
Expected returns \((E(R))\) are defined as: \[E(R) = \sum_{s=1}^K p_s \times R_s\]
Variance is defined as: \[\sigma^2=\sum_{s=1}^K p_s \times [R_s-E(R)]^2\]
Standard deviation \((\sigma)\) = \(\sqrt{\sigma^2}\)
| Scenario | Probability | Return |
|---|---|---|
| Excellent | 25% | 31.00% |
| Good | 45% | 14.00% |
| Poor | 25% | −6.75% |
| Crash | 5% | −52.00% |
\[ \begin{align} E(R) &= \sum_{s=1}^4 p_s \times R_s \\ &= (0.25 \times 0.31) + (0.45 \times 0.14) + (0.25 \times -0.0675) + (0.05 \times -0.52) \\ &= 0.0976 \\ &=9.76\% \end{align} \]
| Scenario | Probability | Return |
|---|---|---|
| Excellent | 25% | 31.00% |
| Good | 45% | 14.00% |
| Poor | 25% | −6.75% |
| Crash | 5% | −52.00% |
\[ \begin{align} \sigma^2 &= \sum_{s=1}^4 p_s \times [R_s-E(R)]^2 \\ &= 0.25 \times (0.31-0.0976)^2 + 0.45 \times (0.14-0.0976)^2 + \\ & \qquad 0.25 \times (-0.0675-0.0976)^2 + 0.05 \times (-0.52-0.0976)^2 \\ &= 0.038\\ \sigma &= \sqrt{0.038}=0.1949=19.49\%\\ \end{align} \]
For a portfolio with two risky assets, the expected return and variance equations are: \[E(R_p) = w_1 E(R_1) + w_2 E(R_2)\]
Correlation coefficient between two assets:
Need to estimate two expected return, two variances and one covariance/correlation